I wouldnt use oven cleaner either. It is simply lye, and it damages the wood fibers.
Black spots? You sure you wasnt chewin that baccy again and droolin on it?
Like the other guys said, you dont want to completely strip the stock, just clean the checkering, I'd thin some turpentine with paint thinner and then just go easy on that checkering with a tooth brush, get it clean and then wipe the excess off. If you have an oil finish the turps wont harm it. All you want to do is get the dirt and grease and dead skin out of the checkering. Even then you may find the tops of the checkering worn down. If it is important, it can be recut by someone who knows what they are doing.